1. Field of the Invention
The present invention generally relates to an uncomplicated technique for measuring the size of plasma gel fibers and, more particularly, to a method for determining the fibrin fiber mass/length ratio from a single measurement of gel optical density.
2. Description of the Prior Art
When injury occurs, blood clots to prevent blood loss. Clots contain erythrocytes and platelets but the primary clot scaffolding is interconnected fibrin fibers. Formation of the clot scaffolding is begun by a complex series of proenzyme-enzyme reactions that are initiated upon tissue injury. These reactions result in the conversion of prothrombin into thrombin. Once activated, thrombin cleaves two pairs of small peptides (fibrinopeptides A and B) from the alpha and beta chains respectively of the plasma protein fibrinogen. Once these negatively charged peptides are removed, the repulsive forces that normally prevent fibrinogen aggregation are reduced and new binding sites are exposed. As a consequence, fibrinogen devoid of its fibrinopeptides, termed fibrin monomer, spontaneously assembles into a three dimensional network. This process of polymerization is accomplished by both side-to-side and end-to-end stacking of fibrin monomer units. The initial structure is a long thin protofibrile only two monomer units wide. As the protofibriles reach a critical length, they begin to align themselves along their major axis resulting in larger fibers composed of bundles of protofibriles. A given protofibrile may be involved in one fiber along one portion of its length while being part of another fiber along another portion. As fibers continue to increase in size, virtually all the available fibrin monomer is incorporated into the network. The final result is a space-filling structure composed of fibrin fibers separated by relatively empty spaces. The network is initially stabilized only by hydrogen bonding. The activation of Factor XIII by thrombin permits the introduction of covalent bonds between the monomer units resulting in a network of enhanced strength.
The morphology of fibrin is important to its function. The network can be thought of as a series of interconnecting rods separated by intervening spaces or pores. These pores may be relatively open or may be filled with red cells. The permeability of clots is a function of pore size which can be directly measured by perfusing liquid through a clot. Pore size can also be estimated as a function of fiber size. If the amount of fibrin in a given volume remains constant, pore size will increase as fiber size or mass/length ratio increases. When fibrin is concentrated in a few large fibers, the distances or voids separating them will be increased.
Fiber thickness is determined by the balance of electrochemical forces favoring end-to-end and side-to-side alignment of fibrin monomers during gelation. When end-to-end alignment is favored, long thin fibers are formed. When side-to-side alignment is favored, thick fibers form. Microenvironmental alterations are capable of producing profound effects on fibrin assembly and fiber structure. Low ionic strength, low pH, and the presence of divalent cations favor thick fiber formation. Some cellular release products such as leukocyte cationic protein and platelet factor 4 also favor thick fiber formation. Plasma proteins have variable effects. IgG favors thin fiber formation while albumin has minimal impact. In plasma, the composite of all these influences results in the production of larger fibers than those formed in purified solutions. Causes of altered plasma fibrin fiber structure include: elevated immunoglobulin levels; fibrin polymerization inhibitors such as fibrin degradation products; dysfibrinogenemias--either primary or secondary to hepatic insufficiency; and interference by drugs such as hydroxethylstarch and dextran. Given the dependence of fibrin structure on its microenvironment, additional clot altering variables will undoubtedly be recognized as fibrin structural analysis becomes routinely available.
While normal fibrin structure is obviously critical to clot performance, quantitative measures of fibrin structure have been unavailable. The reporting of plasma clot structure remains a rather qualitative endeavor. Such terms as whispy and flimsy are still used to describe plasma clots which do not appear "normal" in the eye of the technician. Previous attempts to be more quantitative regarding clot structure have centered primarily on elasticity measurements. While intuitively pleasing, a strong clot being better than a weak one, these measurements are not generally available and their interpretation is not routine.
In our laboratory, we have derived methods which allow measurement of gel fiber size. The methods, based on classical light scattering techniques, measure the average mass/length ratio (.mu.) of the gel fibers. .mu. is a measure of fiber size and, if fiber density is uniform, is directly proportional to the second power of the fiber radius. Thus, larger .mu. values correlate with larger fiber cross sectional area. While useful in purified protein gel systems, light scattering techniques are not applicable to complex systems such as plasma. To overcome this problem, we modified our procedures to allow measurement of .mu. from turbidity. Since turbidity is the sum (integral over all angles) of all scattered light, the value of .mu. should be derivable from turbidity measurements. Integration of light scattering equations yielded a new set of equations which predicted that turbidity (.tau.) would be a reciprocal function of the third power of the wavelength (.lambda.). The equations indicated that a plot of .tau. versus 1/.lambda..sup.3 would be linear and that the slope of such a plot would be proportional to .mu..
The derivation of equations used to calculate the fiber mass/length ratio (.mu.) from the wavelength dependence of the gel turbidity is as follows:
The turbidity, .tau., of a solution is a measure of the decrease in intensity of transmitted light due to scattering and can be calculated by integration of the scattered intensity over all possible angles. For solutions, the scattered intensity depends on the angle, .theta., between the primary beam and the scattering direction. Hence, equations (1) and (2) are presented: EQU .tau.=2.pi.d.sup.2 (i.sub..theta. /l.sub.o)sin.theta./de EQU .sub..theta. /l.sub.o =R.sub.74 (1+cos.sup.2 .theta.)/.lambda.d.sup.2
where i.sub..theta. is the scattered intensity per unit of volume, l.sub.o is the intensity of the incident beam, and d is the distance between scattering volume and detector. The Rayleigh ratio R.sub..theta. depends on the mass and dimensions of the particles. According to theory, for very long and thin rodlike particles, the scattering factor is given by equation (3): EQU R.sub..theta. =ck.lambda..mu./4nsin(.theta./2)
where c is the concentration, .lambda. is the wavelength in vacuo, .mu. is the mass/length ratio of the fibers (dalton/cm), and n is the refractive index of the solution. The wave vector K is constant for any given wavelength and is given by equation (4): EQU K=2.pi..sup.2 n.sup.2 (dn/dc).sup.2 /N.lambda..sup.4
where dn/dc is the specific refractive index increment of the solute in the solvent and N is Avogadro's number.
It has been shown that equations 2-4 give a good description of experimentally observed light scattering by fibrin fibers. Substituting equations 2 and 3 into equation 1 and integrating, one obtains equation (5): EQU .tau.=(44/15).pi.Kc.lambda..mu./n
Since K, .lambda., and n are known parameters, one can in principle calculate the weight average mass/length ratio of the fibers from the measured turbidity of a gel of known concentration. Equation 5 also implies that the turbidity should vary as 1/.lambda..sup.3, if we neglect the sight wavelength dependence of n and of dn/dc.
FIG. 1 shows the wavelength dependence of the turbidity of four fibrin gels wherein each gel has fibrin concentration of 1.0 mg/mL and a thrombin concentration of 1.25 NIH units/mL. Each of the gels contains a different concentration of NaCl and was formed directly in polystyrene cuvettes as described below. The prediction that the turbidity should vary as 1/.lambda..sup.3 is confirmed in FIG. 1, wherein plots of .tau. vs 1/.lambda..sup.3 for fibrin gels formed with varying salt concentrations yields straight line relationships.
FIG. 2 shows a correlation of the mass/length ratios (in daltons/cm) calculated from turbidity and from the 90.degree. scattering intensity, both at 632.8 nm, of a number of fibrin gels. Gels were formed using varying amounts of thrombin to provide a spectrum of .mu. values. Mass/length ratios calculated from turbidity are plotted against those calculated from the 90.degree. scattering intensity. The technique of calculating the .mu. from a measurement of turbidity is in agreement with the more difficult (and more limited) classical light scattering technique. The excellent agreement for low turbidity gels is obvious.
The turbidity of fibrin gels is proportional to 1/.lambda..sup.3 over a considerable wavelength range but the proportionality breaks down for gels with very large mass/length ratios (.mu.). The breakdown occurs because the diameters of fibers with large mass/length ratios (.mu.) are not small compared with the wavelength of the incident light. Whenever this is the case, the turbidity will not be as large as calculated with equation (5). In these cases the following relation, embodied in equation (6), becomes appropriate: EQU (44/15).pi.Kc.lambda./n.tau.=.mu..sup.- 1(1+184.pi..sup.2 .sigma..sup.2 n.sup.2 /77.lambda..sup.2 . . . )
This result is obtained by integrating a similar expansion for the light scattering intensity in powers of sin(.theta./2)/.lambda.. It follows that if one plots c/.tau..lambda..sup.3 as a function of 1/.lambda..sup.2, then the intercept of the plot can be used to calculate the mass/length ratio (.mu.), while the ratio of the initial slope and the intercept of the plot can be used to calculate the square of an average dimension, .sigma. (z-averaged radius of gyration), which is determined by size and shape of the fibers' cross section. This kind of plot if analogous to the plot of Kc/R.sub..theta. vs sin.sup.2 (.theta./2) commonly used to obtain molecular weight and radius of gyration from light scattering of molecularly dispersed particles. For cylindrical fibers of radius .GAMMA., one may use the series expansion, equation (7), with: EQU .sigma..sup.2 =.GAMMA..sup.2 /2
If one assumes that 1/.tau..lambda..sup.3 simply varies linearly with 1/.lambda..sup.2 and neglects higher order terms, the calculated slope will not be seriously in error, as long as no observations are used for which 1/.tau..lambda..sup.3 is greater than twice its extrapolated value.
FIG. 3 is a plot of c/.tau..lambda..sup.3 vs 1/.lambda..sup.2 for several turbid fibrin gels formed with varying amounts of thrombin (indicated at the left in NIH units/mL). The data have been fitted with straight lines. The intercept of these lines is proportional to the reciprocal of the mass/length (.mu.) ratio, and the ratio of slope and intercept is proportional to the square of the radius of the fibers. The solutions each contained 1 mg/mL fibrin and 0.1 M NaCl, pH 7.4. The thrombin concentration is indicated by each curve. As predicted, the plots are straight lines. The intercept of these lines is proportional to the reciprocal of the mass/length (.mu.) ratio, and the ratio of slope and intercept is proportional to the square of the radius of the fibers.
The above confirms the validity of these equations. We have subsequently demonstrated their applicability to plasma systems. We and others have demonstrated the reproducibility of and clinical utility of this parameter in describing patient clot structure. Up to this time, the use of the turbidity technique has been restricted to facilities and laboratories equipped with scanning spectrophotometers. The expense of such equipment has limited the widespread measurement of this useful parameter.